1. Technical Field
This invention generally pertains to the measurement of the distance to a remote object. More particularly, it concerns passive monostatic ranging, that is, measuring distance using electromagnetic or acoustic waves without illuminating, or querying, the object with electromagnetic or acoustic energy, and without involving spatial parallax. A fundamentally new way is disclosed for extracting distance information from the spectral phase profile, i.e. the phase distribution across a set of frequencies, in a received signal, without requiring it to be reflected or transponded. The invention more specifically concerns extraction of this information as a hitherto unrecognized effect of the wave nature of electromagnetism and sound similar to the Doppler effect, but using only the instantaneous source distance and receiver-side operations.
2. Brief Description of the Prior Art
Problems of dependence on known illumination. Hitherto, the only ways to measure the distance r to a target have been by parallax, triangulation, or timing an echo or a returned transponder signal from the target, called the round trip time (RTT) measurement. All known radar techniques are primarily based on the timing approach, although parallax is implicitly utilized in some cases, notably synthetic aperture radar (SAR), which provides the imaging of static topographies using a moving platform for the radar.
The timing approach is constrained by problems of scalability, power and antenna size, since illuminating a target at range rmax requires a power P∝rmax4 and equivalently, the range is limited to rmax∝P1/4 for an available power P. The power requirement can be alleviated by improving the receiver technology, using very low noise receivers and large antennas to collect more power. For example, A Freeman and E Nielsen of JPL have proposed a radar for mapping Kuiper Belt objects using a transmitter power of 10 MW, but located in space and with an antenna diameter of 1 km.
In all of the prior art, the need for illumination severely constrains radar technology. Even with very high power ground stations in NASA's Deep Space Network, accurate ranging of spacecraft in deep space has been possible only by using the onboard telemetry transponder to return a modulated signal instead of an echo, and thus reducing the power requirement to rmax2. The method was described by P L Bender and M A Vincent in the August 1989 NASA Technical Report N90-19940 12-90, titled “Small Mercury Relativity Orbiter” and paper “Orbit determination and gravitational field accuracy for a Mercury transponder satellite”, in Journal of Geophysical Research, volume 95, pages 21357–21361, December 1990. Methods depending on transponders can be useful only for specially equipped cooperative targets, however. Other reasons, such as avoiding giving away the radar's location, significantly add to the motivation for passive radar technologies.
Unfortunately, existing passive systems are again dependent on illumination from known source like radio and television broadcasting stations, as first described in the U.S. Pat. No. 3,812,493, issued in 1974, and in the recent years, from cellular telephone base stations. Secondly, the large number of illuminating sources and the complexity of their signals makes the extraction of useful information from the reflections an extremely difficult computational problem. Further, direct signals must also be collected from each of the illuminating sources for phase correlation with the target's echo, which means additional antennas and infrastructure. In any case, the method is limited to regions of the earth where there are adequate illuminating sources, and also cannot be employed for ubiquitous applications being envisaged, like ground vehicular guidance and collision avoidance, nor for earth orbit or deep space tracking, where the illumination is generally absent.
Another now well known terrestrial application concerns the requirement, in cellular telephone and wireless networking technologies, to limit the power transmitted by a mobile device, primarily so that the frequencies can be reused in other nearby “cells”, and also to conserve its battery. RTT measurement is the only method currently available and requires each mobile device to transmit at least once, regardless of whether the base station or the mobile device measures the RTT.
A ranging method that does not depend on illumination, and would instead use the target's own emissions would be desirable both as an alternative in existing radar applications as well as for novel applications that are currently impossible or impractical. Its range would be governed by the inverse square law of one-way propagation in free space, instead of the fourth power law, and it would be therefore usable over much longer distances. Since no phase correlations with illumination sources would be required, the computation, if any, should be vastly simpler than that in current passive radars. A cellular device employing it would be able to gauge its distance from the nearest base station accurately from the latter's transmissions. In optical fibres and transmission lines in integrated circuit chips, degradation or breakage could be detected with absolutely no interruption of service, scheduled or otherwise.
Use of chirp or ramp signals. One way to describe the present invention is in terms of a signal with an exponentially increasing or decreasing frequency. Linear variation of frequency as ω(t)=ω0+at, commonly called chirp in radar texts, in allusion to the acoustic echo location method used by bats. The RTT δt is then directly obtained by measuring the frequency δ(ω)=αδt of the beat signal that results by summing the echo, of frequency ω(t)=ω0+α(t−δt), with the instantaneous outgoing chirp signal. Note that ramping of the frequency is preferable to ramping of the amplitude because amplitude extraction is more vulnerable to noise and other problems. In both cases, the result must be corrected for the target velocity, which must be separately determined. A simple method for this is to change the slope α of the ramp, since the Doppler shift is invariant of α and can then be eliminated by comparing the results. However, these prior uses of chirps are for simplifying RTT measurement rather than eliminating it, and do not enable passive operation.Wavelets analysis. A related description of the present invention is as a technique involving continuously varying frequency or time scales. A powerful means for analyzing multi-scale phenomena is now available in wavelet transforms. A fundamental difference remains, however, that the wavelet techniques are concerned with the scale distribution of the source signal, which cannot depend on the receiver's distance.
In the present invention, the scale variance is incorporated in the receiver, and the distance information is then associated with each individual frequency observed, independently of wavelet or other radar processing techniques that may be applied to the observations.
Variable tuners and diffraction gratings have been around for many decades as well, so it is reasonable to expect at least accidental observations of the inventive mechanism in the prior art. None is mentioned in the literature, however, likely due to several reasons which will become clearer from the Detailed Description.
The first problem is that without the requisite manner of control which will be specified, the mechanism would produce frequency shifts in the received waves proportional to source distances. The net result for a typical input signal comprising contributions from multiple sources is a dispersion that bears no discernible correlation to any of the individual input frequencies, and is therefore easily mistaken for transitional noise. This generally explains why the invention was hitherto unobvious from accidental observations, for example, from resonators like guitar strings or Fabry-Perot cavities of lasers while being setup or tuned.
A second problem particularly limiting the accidental category is that the invention requires an exponential profile of variation, or else the result is an even more complex form of dispersion from which the distance correlations are all the more difficult to recognize. It is hardly surprising, therefore, that transitory behaviour of tuned systems and spectrometers have been mostly ignored in prior art, with the exception of frequency modulation systems in communication. In the latter case, not only are the transition rates linear and limited in magnitude, but the modulation as such is applied at the source itself, so the possibility of distinguishing distance correlations is nonexistent.
With the controlled transitions now provided by variable tuners and gratings, two problems have served to limit prior discovery, the first being that all such variable systems, like frequency modulation, are designed primarily for linear variation. The second is that most such devices, especially the more accurate ones, are designed for controlling static selection of wavelength or frequency, whereas the invention concerns changing of the selection during observation. Most communication systems use phase-locked loops (PLLs) that prevent variation of the selection from the incoming carrier. Continuously variable diffraction gratings are available in the form of acousto-optic (Bragg) cells, but in this case, the grating is formed by an acoustic wave whose wavelength cannot be varied instantaneously across the spatial observation window.
A fourth class of problems that hitherto prevented discovery is especially clear in the case of digital signal processing commonly applied to both acoustic and radio signals. To begin with, the theoretical treatment was hitherto exclusively in terms of amplitudes, frequencies and phases, so the the source distance would be hidden in the phases and the start-time delay. Secondly, the data is conceptually decoupled from the sources and their distances by sampling and digitization, making a reverse correlation with the source distances all the more unintuitive. Thirdly, even with analogue recordings, the source distances generally manifest only as start-up delays in the time domain, with no real value as the source of the distance information. In the present invention, logical connection to the physical distance is maintained, as will become clear, by applying the inventive procedure only at the frontend of the receiver, and the source of the distance information is the spectral phase profile, applicable to a continuous signal, rather than the start-up delay, which would have required an RTT reference once again.
Availability of source distance information in the phase spectrum of a received signal was the subject of an imaging method described in the paper “Radar imaging by Fourier inversion” by V. Guruprasad and A. K. Bhattacharyya, in the Proceedings of Union Radio Science Internationale, 1986. The paper concerned imaging in a pulse radar in which the target is illuminated with pulses at regular intervals T. The illuminating spectrum contains harmonics at frequency intervals of 1/T as a result. Over the relatively small operating band, variations in the atmospheric dispersion can be ignored, so that the different frequencies propagate at almost the same speed c. Their phases vary at different rates, however, since a frequency ω by definition relates to phase φ as ω=dφ/dt≡cdφ/dr, where r measures the path length travelled. Target features are then resolved along the radial direction from the radar by a simple Fourier inversion of the echo spectrum. Together with “aspect angle diversity” generally available from moving targets such as aircraft, this suffices to yield a distinguishing two-dimensional image of the electromagnetic features of the target.
This prior method thus extracts incremental distance information pertaining to displacements δr between the target's features, rather than the full distance r from the source. In hindsight, it suggests likely presence of this information in the phase spectrum, as the limitation that prevented its extraction in the prior method was simply the operating bandwidth. Denoting the smallest resolvable phase difference as Δφ, typically π rad or better, the method differentiates objects or features Δr=cΔφ/ω apart. Therefore, for the full range r to the target, we would need low enough frequencies ω≈cΔφ/r, and if such frequencies were usable, we would not need the phase, or timing, reference of the illuminating pulses. Another reason for this conclusion is that sources or scattering centres form the centres of curvature of the spatial wavefronts, which are defined by phase contours, hence the source location information is encoded in every wavefront. This is precisely the information involved in the image reconstructed by a hologram, except that holographic reconstruction uses interference between multiple paths instead of frequencies.
The principal limitations of the modified pulse radar method described above are its dependence on long wavelengths, requiring λ=O(r), and the problem of aliases, due to recurrence of the same phase at multiples of the wavelength. The method appears usable for underwater sonar, but numerous other techniques are well developed for this case. With electromagnetic waves, the method is unusable outside of a narrow range of distances because of the very high value of c: with Δφ=π, it requires interrogation (illumination) at frequencies of 60 GHz at r=100 m, 6 GHz at 1 km and 600 MHz at 10 km. A method without a linear dependence on the wavelength would be clearly desirable. Intuitively, one would expect a heterodyning or modulation technique to be the answer, and NASA's deep space ranging technique mentioned above is a first step in this direction, although usable only for the small class of transponding targets.
Use of frequency instead of time reference. NASA's deep space technique includes tracking of residual Doppler shift in the modulated return signal, which has particularly revealed an “unmodelled acceleration” in “all six missions” to date involving spin-stabilized spacecraft, as reported by J. D. Anderson and others in Physical Review D, vol. 65, April 2002. Although the residual shift was measured relative to the original transmitted signal in this case, as in most existing Doppler radars, use of atomic and nuclear spectral lines to determine Doppler shifts is common practice in many fields. More particularly, normalized shift factors z=δω/ω are used in astrophysics as distance indicators on the cosmological scale.
The basic difficulty in using the same principle on a terrestrial scale is of course that measurable redshifts are only seen for very distant galaxies, meaning that the cosmological expansion is too slow to be usable for distance measurements even at inter-galactic scales. According to the Einstein-deSitter model, gravitational deceleration would have slowed the expansion down to the order of 10−41 m/s on the scale of earth's orbit (1 AU 150×106 km), as shown by Cooperstock et al. in the Astrophysical Journal, vol. 503, pages 61–68, 1998. One explanation of why the relativistic expansion cannot occur on short distances is that if the atoms of an observer were to be expanding at the same rate, the expansion itself would be unobservable, as discussed, for example, in Misner, Thorne and Wheeler's Gravitation, Freeman, 1973 (page 719).
Incidentally, several researchers have pointed out that the Pioneer acceleration appears to be indication of the expansion persisting undiminished from its large scale value H0≈67 km s−1 Mpc−1≈2.17×10−18 s−1 on the solar system scale. The expansion is known to be undiminished on the scale of our local group of galaxies, posing the dual problems of “flatness”, reflecting a remarkable balance between classically expected gravitational deceleration and the acceleration, and “quietness”, as the repulsive force presumably responsible does not present fluctuations consistent with a gas-like pressure. As a possible alternative explanation which is cited by Anderson et al. and led to the present invention, it was suggested in manuscript astro-ph/9907363 posted on the preprint archive server http://www.arxiv.org that the cause could even be simply terrestrial, describing complete empirical consistency of planetary, lunar and terrestrial data. Assuming this hypothesis to be valid, the available expansion rate would still be only O(10−18) s−1.
Further, even if the cosmological expansion were large enough to be usable for terrestrial measurements, we would still be confined to a smaller range of scales than with a method that did not depend on a natural phenomena but instead involved a human-controllable parameter.
Use of receiver modification. The present invention was inspired by a detailed analysis and alternative explanation of the Pioneers' anomalous acceleration in astro-ph/9907363 and gr-qc/0005090, viz slow but steady shrinkage of instruments on earth and in low earth orbits due to ordinary creep under the compressive force of earth's gravity and the tidal action of the moon and the sun. A third manuscript gr-qc/0005014 gives a first-principles derivation of special and general relativity from analysis of the role of the instrument scales in physical measurements and overcomes the unobservability problem with expansion on short scale that limits the relativistic theory. This was called “space-time elasticity theory” by Anderson et al., but the key mechanism is inelastic and macroscopic, and the second aspect enables general use.
The theory also fundamentally differs from a more naïve relativistic intuition, attributed to Eddington, that a uniform expansion of the universe would be equivalent to a uniform shrinkage of every atom, in that the scale of the atomic structure cannot be affected by macroscopic phenomena like creep. More significantly:                The creep rate would be different onboard a spacecraft, on another planet or in another solar system, and further, vary with time in all cases as the tidal stresses evolve.        The cosmological expansion and acceleration would be virtual, with different values depending on the platform they are measured from.        Both quantities would also vary slowly at each location, and exhibit directionality correlating with the local tidal stresses. From aboard the Pioneer spacecraft, the universe would have appeared to be static along the spacecraft's spin axis and contracting, with the acceleration, in transverse directions.        
Both quantities would be more specifically determined by the negative of the observer's local, instantaneous creep rate and its square, respectively. This relation had been derived some years before the discovery of the acceleration in 1998. The corresponding variation between ground and deep space clocks revealed by the Pioneer anomaly, which had seemed hopeless to propose, had been anticipated months before NASA's first report in October, 1998. The same relation holds for the present invention, but the creep is as unusable for general ranging purposes as the cosmological expansion, for the same reasons of smallness and uncontrollability.
The creep hypothesis had presented a few secondary difficulties in the past, notably the consistency of the current cosmological measurements between telescopes of different constructions and at different latitudes, including those in space, such as the Hubble. A related difficulty was that the difference between the residual anomalies of the two Pioneer spacecraft had to be attributed to difference in the galactic tidal action, which would be several orders smaller than the residual difference. Another difficulty lay in explaining the apparent continuity of the Hubble redshifts, as the required creep rate corresponds to a fraction of a nuclear diameter over the course of a second in any reasonably sized telescope. These difficulties have now been resolved and the solutions will be briefly discussed in the Detailed Description to further illustrate the mechanism of the present invention, which also provides a means for measuring such small creep rates for the first time.
Relation to quantum theoretic notions. Following Einstein's theory of photoelectricity, a corpuscular view of light and particles has become pervasive. According to this view, the wave nature manifests only in matters directly concerning phase, such as diffraction and the Aharanov-Bohm effect of the magnetic vector potential A on particulate diffraction patterns, and even then, only statistically, since the Schrödinger wave equation involves to probability amplitudes instead of actual particles. Consequently, it has become usual to think of a photon as the monochromatic energy quantum of Einstein's theory, given by Planck's quantization rule E=hν, where ν is the frequency. Correspondingly, the thermal spread of spectral lines is commonly regarded as primarily statistical, with individual photons still representing single frequencies.
There are two basic discrepancies within this view which have hitherto defied detailed treatment:                First, as familiar to astronomers studying very distant galaxies, there are steady sources whose pictures are constructed by counting individual photons. The spectral spread cannot be zero for an individual detected photon because a pure sinusoid, by definition, cannot end in the detector. The very fact that the photon is detected thus contradicts the corpuscular notion of intrinsic quantization of the incoming radiation into monochromatic energy quanta.        This issue is distinct from the relativistic question of the speed of information, which would be associated with the velocity of the received photons as a group—the problem concerns the very transfer of individual energy quanta. Treating them as wavepackets would again question their monochromaticity.        The second discrepancy is the associated idea that source distance information can be present in received radiation only as the spatial curvature of the wavefront, which requires multistatic reception to exploit, or the inverse-square law intensity decay, which can be exploited only for “standard candles” of known source intensities. The presence of source distance information in phase envelopes, as revealed by pulse radar imaging, has been unobvious because it cannot be regarded as a statistical result, given that the statistical nature of quantum wavefunctions concerns their amplitudes rather than their phases.        
The only solution to the first problem is to return to the pre-Einstein notion of photons as energy transitions at the detector. This not only preserves Planck's quantization, but does actually explain the very properties of photoelectricity that had led to Einstein's theory and its validation by Millikan (“A Direct Photoelectric Determination of Planck's h”, Physical Review, vol. 7, pages 355–388, 1916). The near-instantaneous response is accurately modelled in the subsequently developed quantum treatment primarily in terms of the detector states. In the second quantization formalism of quantum electrodynamics, which most closely represents the intrinsic quantization notion, photons constitute standing or travelling wave modes of the overall radiation field, rather than isolated packets of radiant energy.
In this refined view, the present invention concerns detector state transition events representing photons that are inherently nonsinusoidal, and therefore capable of bearing distance information. There is no loss of generality either, as will become clear. These concerns are, of course, irrelevant in acoustic applications.
Use of atmospheric characteristics. Other passive methods for determining source distances have been described in U.S. Pat. No. 5,894,343, issued 13 Apr. 1999 to H A French of the UK, and other patents referenced in that patent. These methods exploit atmospheric effects on the source spectra to gauge the distances, and are therefore limited to thermal sources emitting blackbody spectral distribution at elevated temperatures, and to atmospheric ranges with known behaviour.